Disk to Plane

Edit and compile if you like:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
\documentclass[tikz,svgnames]{standalone}
\usepackage{amsmath,amssymb}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[
    thick, font = \scriptsize,
    circ/.style ={circle, fill = gray, draw = gray, inner sep = 1pt}
  ]
  \def\yaxis{2}
  \draw [<->] (-2, 0) -- (2, 0) node (from)[anchor = west]{$x$};
  \draw [<->] (0, -\yaxis) -- (0, \yaxis) node [anchor = south]{$y$};
  \draw [->] (from) (2.75,0) --++(0:1.5) node [anchor = south, midway]{$\begin{aligned}
        z & = S(w) \\
          & =\textstyle \frac{w + i}{i w + 1}
      \end{aligned}$};
  \node (CI) at (0, 0) [circ, fill = gray, opacity = 0.1, minimum size = \yaxis cm]{};
  \begin{scope}[decoration={
          markings,
          mark=at position 0.25 with {\arrow{>}},
          mark=at position 0.75 with {\arrow{>}}}
    ]
    \draw[DarkBlue,postaction={decorate}] (0,-1) arc (-90:90:1);
    \draw[DarkRed,postaction={decorate}] (0,-1) arc (270:90:1);
  \end{scope}
  \node [pin={[pin distance=30,inner sep=1pt]20:$w_0 = 0$}] {};
  \node at (CI.east) [anchor = north] {$w_1 = 1$};
  \node at (CI.south) [anchor = west] {$w_2 = -i$};
  \node at (CI.west) [anchor = north] {$w_3 = -1$};
  \node at (CI.north) [anchor = south west] {$w_4 = i$};
  \node at (CI.110) [anchor = north east, below = 2pt]{$\mathbb{D}^2$};
  \foreach \x in {west, center, east, south, north}{
      \node [circ] at (CI.\x) {};
    };
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX